WSEAS TRANSACTIONS on CIRCUITS and SYSTEMS
Jium-Ming Lin, Po-Kuang Chang
Intelligent Ziegler-Nichols-Based Fuzzy Controller Design for Mobile
Satellite Antenna Tracking System with Parameter Variations Effect
JIUM-MING LIN and PO-KUANG CHANG
Ph.D. Program in Engineering Science, College of Engineering
Chung-Hua University
707, Sec. 2 Wu-Fu Rd. Hsin-Chu
TAIWAN, R. O. C.
jmlin@chu.edu.tw http://www.cm.chu.edu.tw/files/11-1017-2419.php
Abstract: - This research applied both the traditional, Ziegler-Nichols-based and Ziegler-Nichols-based
fuzzy control methods for mobile satellite antenna tracking system design. Firstly, the antenna tracking and the
stabilization loops were roughly designed according to the traditional bandwidth and phase margin
requirements. However, the performances would be degraded if the tacking loop gain is reduced due to
parameter variations. On the other hand both Ziegler-Nichols-based PID-type and Ziegler-Nichols-based
fuzzy controllers were also applied in the tracking loop for refinement. But we can find only the fuzzy
controller were better for both low and high antenna tracking loop gains, and the tracking loop gain parameter
variations effect can be reduced.
Key-Words: - Tracking Loop, Stabilization loop, PD-type Fuzzy Controller; PI Compensator
degradation effect into consideration, then the
performances becomes worse for the cases of lower
tracking loop gains.
On the other hand both Ziegler-Nichols-based
PID-type [8] and Ziegler-Nichols-based fuzzy
controllers [9-10] were also applied in the tracking
loop for refinement. But we can find only the fuzzy
controller were better for both low and high antenna
tracking loop gains, and the tracking loop gain
parameter variations effect can be reduced. By the
way to reduce computer loading the simplified
triangular distribution relationship functions of the
fuzzy controller was applied.
The organization of this paper is as follows: the
first section is introduction. The second one is for
traditional design of antenna tracking and
stabilization loops. The antenna performance
analyses with a traditional design are given in
Section 3. The PD-type fuzzy controller design and
performance analyses are given in Section 4. The
last part is the conclusions.
1 Introduction
To cope with the satellite Ka-band and broadband
mobile communication requirements, the capacity is
five times of Ku-band before. The mobile antenna
needs to lock on the satellite in spite of disturbances,
thus the performances of antenna tracking and
pointing precision as well as stabilization should be
raised [1-3]. The traditional PI (Proportion and
Integration) compensator was applied for the
tracking and stabilization loops design of mobile
antennas to lock on the satellites [4]. The fuzzy
controller was applied for the tracking loop design
[5-6], and the relationship functions of Gaussian
distribution were applied for six degrees of freedom
simulation, thus the computation loading was very
large. In addition, the noise and wind disturbance
was taken into antenna design consideration.
However, the parameter variations effects were not
considered in the methods aforementioned.
In this paper firstly we use a simplified model for
the antenna control system design [7-8], the antenna
tracking and the stabilization loops were roughly
designed with the traditional bandwidth and phase
margin design rules to obtain the key parameters of
antenna tracking and stabilization loops. The
stabilization loop was designed by using proportion
and PI compensators for comparison. Noted the
performances with PI compensation method were
better. However, if taking tracking loop gain
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2 Traditional Antenna System Design
The detailed block diagram of a satellite antenna
tracking system is in Fig. 1, in which both tracking
and stabilization loops as well as pitch, roll and yaw
coupling effects are taking into consideration [7]. It
is very complicate and difficult to obtain the key
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Jium-Ming Lin, Po-Kuang Chang
parameters for analyses and simulation. Thus in
general a simplified pitch or yaw model of antenna
control system is applied to speed up the design and
obtaining the key parameters, in which the tracking
loop is modelled as a simple gain, and the
stabilization loop is replaced by a pure integration,
or PI compensators as in Figs. 2 and 3. Then this
research made a roughly designed first according to
the bandwidth and phase margin requirements to
obtain the key parameters of antenna tracking and
stabilization loops. The stabilization loop was
designed by using proportion and PI compensators
for comparison as shown in Figs. 2 and 3. The
tracking loop time constant (Tc) is set as 0.1 seconds
of the practical value for the bandwidth requirement.
2.1 Stabilization Loop Compensator Design
2.1.1 Pure integration compensator
Firstly, the stabilization loop is designed with pure
integration compensator. Let the integrator gain (K1)
of stabilization loop be 25, 50, 75 and 100,
respectively, then the Bode plots are in Fig. 4. The
gain margins are ∞. Although the phase margin
would be increased with larger K1, the increasing
rate approaches saturation for K1=100. So we can
set K1=100 for the initial design.
2.1.2 PI compensator
Secondly, the PI compensator is applied for the
stabilization loop design. T he gains of the
proportion and integration terms are denoted as K0
Fig. 1 The detailed block diagram of the antenna control system.
Fig. 2 The block diagrams of antenna stabilization
loop with a pure integration compensator.
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Fig. 3 The block diagrams of antenna stabilization
loop with a PI compensator.
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Fig. 4 Bode plots for K1 are as 25, 50, 75 and 100 for the stabilization loop be a pure integration compensator.
and K1, respectively. Fig. 5 shows the Bode plots
for several K0’s with Tc=0.1 and K1=100. The
phase margin is larger for K0=5. Fig. 6 shows that
the phase margin is insensitive with K1 (T=0.1 and
K0=5), but the steady-state error can be eliminated
with the larger K1’s. By some trial-and-error one
can see that the phase margins are larger, say 132°
and 133°, for the cases with K0=5, K1=50, Tc=0.1
and K0=5, K1=25, Tc=0.2, respectively. The former
is chosen for faster response and easy of realization.
3 Performance of Traditional Design
In this section the antenna performance is analyzed
by simulation with the block diagram in Fig. 7. The
input line-of-sight angle is a triangle one with
amplitude and period respectively as 1 radian and 5
seconds. It can be seen that the gimbal angle can
track with the input line-of sight angle as in Fig.8,
thus the performance is very good.
However, in general there is tracking loop gain
parameter variation due to the pointing disturbance.
Fig. 5 Bode plots for several K0’s with Tc=0.1 and K1=100 for the stabilization loop be a PI compensator.
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Fig. 6 Bode plots for several K1’s with K0=5 for the stabilization loop be a PI compensator.
Fig. 7 Block diagram of antenna system by the traditional control design method.
Fig. 8 Gimbal angle output with Tc=0.1 for the antenna system designed by the traditional method.
The simulation results with this tracking loop gain
reduced effect are shown in Figs. 9 and 10 for the
parameter Tc changing from 0.1 to 1 and 1.5,
respectively. It can be seen that the tracking
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performances of gimbal angles are reduced. Thus
the traditional method would not be applied for the
systems with lower tracking loop gains.
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Fig. 9 Gimbal angle output with Tc=1 for the antenna system designed by the traditional method.
Fig. 10 Gimbal angle output with T=1.5 for the antenna system designed by the traditional method.
4 Fuzzy Controller Design
4.1 Ziegler-Nichols-Based Controller Design
The first Ziegler-Nichols-Based method [8] is
applied for the design in this section. The method is
to make the unit-step input response as shown in
Fig.11, in which we can determine the gain K of the
steady-state response, the time constant T. In Fig. 11,
both a and L are the coordinates of y- and xintercept points for a line tangent to the curve at the
maximum slope of the unit-step input response.
Then the transfer function of the plant is as follows:
G (s) 
Ke  Ls
Ts  1
Fig .11 The unit-step input response of the antenna
control system with a time delay.
listed in Table 1, in which KP, TI and TD are the gain
coefficients of PID controller and are related to the
magnitudes of a and L. The abbreviation NA stands
for Not Available.
(1)
Then the PID coefficients selection rules are used as
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Table 1 The PID gain coefficients selection rules.
Controller Type
P
PI
PD
PID
KP
1/a
0.9/a
1.2/a
1.2/a
TI
NA
3L
NA
2L
TD
NA
NA
L/2
L/2
So the first step is to apply a unit step input to
the antenna control system in Fig.3, the unit step
response is in Fig.12. One can find that K=1, L=0.3,
and a=0.5. By Table 1 one has the gain coefficients
of PID compensator as: KP=1.2/a≒2.4, TI=2L=0.6
and TD=L/2=0.15. If the input line-of sight is a saw
tooth wave, then the responses for the gimbal angle
for the PI, PD and PID compensators with Tc=0.1
are as shown in Figs.13-15, respectively. We can
see all the results are acceptable. But for Tc=1 we
Fig. 12 The unit-step input response of the system.
can see all the delay effects in the outputs are very
serious as in Figs. 16-18. Finally, for Tc=1.5 we can
see both the delay effects in the outputs are evenly
slow down with the PI, PD and PID compensators
as shown in Figs.19-21, respectively. Thus the
Ziegler- Nichols-based controller cannot be applied.
Fig. 13 Gimbal angle output with Tc=0.1 with Ziegler-Nichols-based PI compensator.
Fig. 14 Gimbal angle output with Tc=0.1 with Ziegler-Nichols-based PD compensator.
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Fig. 15 Gimbal angle output with Tc=0.1 with Ziegler-Nichols-based PID compensator.
Fig. 16 Gimbal angle output with Tc=1 with Ziegler-Nichols-based PI compensator.
Fig. 17 Gimbal angle output with Tc=1 with Ziegler-Nichols-based PD compensator.
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Fig. 18 Gimbal angle output with Tc=1 with Ziegler-Nichols-based PID compensator.
Fig. 19 Gimbal angle output with Tc=1.5 with Ziegler-Nichols-based PI compensator.
Fig. 20 Gimbal angle output with Tc=1.5 with Ziegler-Nichols-based PD compensator.
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Fig. 21 Gimbal angle output with Tc=1.5 with Ziegler-Nichols-based PID compensator.
The detailed cross reference rules for the
inputs and output of the fuzzy controller are
defined in Table 2. According to fuzzy control
design method the relationship functions of
boresight error E, ΔE (deviations of present E
and the previous E), and U (control input) are
defined at first, which are listed in Table 3. To
reduce the computation time the triangular
distribution functions are applied in fuzzy
controller relationship functions calculation
instead of using the traditional Gaussian ones.
4.2 Ziegler-Nichols-Based Fuzzy Controller
In this section the Ziegler-Nichols-based PI, PD
and PID type fuzzy controllers [6-7] are applied in
the tracking loop as in Fig.22. It is well-known that
fuzzy controller is based on the IF-THEN RULE as
follows.
R1: IF E is NB AND ΔE is NB THEN U is NB,
R2: IF E is NB AND ΔE is ZE THEN U is NM,
R3: IF E is NB AND ΔE is PB THEN U is ZE,
R4: IF E is ZE AND ΔE is NB THEN U is NM,
R5: IF E is ZE AND ΔE is ZE THEN U is ZE,
R6: IF E is ZE AND ΔE is PB THEN U is PM,
R7: IF E is PB AND ΔE is NB THEN U is ZE,
R8: IF E is PB AND ΔE is ZE THEN U is PM,
R9: IF E is PB AND ΔE is PB THEN U is PB,
where NB, NM, NS, ZE, PS, PM, and PB
respectively stand for negative big, negative middle,
negative small, zero, positive small, positive middle,
and positive big.
Table 2 Fuzzy controller cross reference rules.
E, ΔE
NB
NM
NS
ZE
PS
PM
PB
NB
NB
NB
NM
NM
NS
NS
ZE
NM
NB
NM
NM
NS
NS
ZE
PS
NS
NM
NM
NS
NS
ZE
PS
PS
ZE
NM
NS
NS
ZE
PS
PS
PM
PS
NS
NS
ZE
PS
PS
PM
PM
PM
NS
ZE
PS
PS
PM
PM
PB
PB
ZE
PS
PS
PM
PM
PB
PB
Then the antenna performance is analyzed by
simulation. Figs.22-24 show the antenna tracking
responses with fuzzy PI, Pd and PID compensator
for Tc to be as 0.1, 1 and 1.5, respectively. It can be
seen that the results are better than those obtained
by using the traditional compensators for all the
three values of Tc.
Fig.22 A fuzzy controller is applied in the tracking
loop design.
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Table 3 Relationship functions of E, ΔE and U.
Item
Parameter E
Parameter ΔE
Parameter U
Negative Big (NB)
[-1 -1 -0.75 -0.3]
[-4.5 -4.5 -3.375 -1.35]
[-12 -12 -9.6 -8.4]
Negative Medium (NM)
[-0.75 -0.3 -0.15]
[-3.375 -1.35 -0.72]
[-9.6 -8.4 -7.2]
Negative Small (NS)
[-0.15 -0.1 0]
[-1 -0.5 0]
[-8.4 -4.8 0]
Zero (ZE)
[-0.05 0 0.05]
[-0.25 0 0.25]
[-4.8 0 4.8]
Positive Small (PS)
[0 0.1 0.15]
[0 0.5 1]
[0 4.8 8.4]
Positive Medium (PM)
[0.15 0.3 0.75]
[0.72 1.35 3.375]
[7.2 8.4 9.6]
Positive Big (PB)
[0.3 0.75 1 1]
[1.35 3.375 4.5 4.5]
[8.4 9.6 12 12]
Fig. 19 Gimbal angle output with T=0.1 with Ziegler-Nichols-based fuzzy PI compensator.
Fig. 19 Gimbal angle output with T=0.1 with Ziegler-Nichols-based fuzzy PD compensator.
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Fig. 19 Gimbal angle output with T=0.1 with Ziegler-Nichols-based fuzzy PID compensator.
Fig. 19 Gimbal angle output with T=1 with Ziegler-Nichols-based fuzzy PI compensator.
Fig. 19 Gimbal angle output with T=1 with Ziegler-Nichols-based fuzzy PD compensator.
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Fig. 19 Gimbal angle output with T=1 with Ziegler-Nichols-based fuzzy PID compensator.
Fig. 19 Gimbal angle output with T=1.5 with Ziegler-Nichols-based fuzzy PI compensator.
Fig. 19 Gimbal angle output with T=1.5 with Ziegler-Nichols-based fuzzy PD compensator.
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Fig. 19 Gimbal angle output with T=1.5 with Ziegler-Nichols-based fuzzy PID compensator.
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[4] V. Jamnejad and A. C. Densmore, A dual frequency
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H. Zhang and D. Liu, Fuzzy Modeling & Fuzzy
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5 Conclusion
This research applied both the traditional compensator
as well as the PD-type fuzzy control methods for mobile
satellite tracking antenna system design. Since the
detailed block diagram of a satellite antenna tracking
system is very lousy, it is very difficult to obtain the key
parameters for analyses and simulation. Thus, a
simplified model of antenna pitching or yawing control
system is applied to speed up the design and obtain the
key parameters. The antenna tracking and the
stabilization loops were designed firstly according to the
traditional bandwidth and phase margin requirements.
However, the performance would be degraded if the
tacking loop gain is reduced due to parameter variations.
On the other hand a PD-type of fuzzy controller was
also applied for the design. It can be seen that the
system performances obtained by the fuzzy controller
were better for not only lower but higher antenna
tracking loop gains. Thus the tracking gain parameter
variations effect can be reduced.
Acknowledgment
This work was supported by the grant of National
Science Council of the Republic of China with the
project number NSC 95-2623-7-216-001-D.
References:
[1] A. C. Densmore and V. Jamnejad, Two WKa-band
mechanically steered and mobile antennas for the
NASA ACTS mobile terminal, Proc. Advanced
Communications Technology Satellite Program
Conference, NASA, Wash., D.C., 1992.
[2] A. C. Densmore and V. Jamnejad, A satellitetracking Ku- and Ka-band mobile vehicle antenna
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